Least Common Multiple (LCM) of 42 and 138
The least common multiple (LCM) of 42 and 138 is 966.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 42 and 138?
First, calculate the GCD of 42 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 138 = 0 remainder 42 |
| 2 | 138 ÷ 42 = 3 remainder 12 |
| 3 | 42 ÷ 12 = 3 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 13 | 1820 |
| 176 and 195 | 34320 |
| 83 and 57 | 4731 |
| 100 and 96 | 2400 |
| 13 and 79 | 1027 |